(a) Draw the triangle with vertices A = (2,2), B = (1,3), and C = (0,0). By regarding it
Chapter 4, Problem 4.4.5(choose chapter or problem)
(a) Draw the triangle with vertices A = (2,2), B = (1,3), and C = (0,0). By regarding it as half of a parallelogram, explain why its area equals area(ABC) = 1 2 det" 2 2 1 3# . (b) Move the third vertex to C = (1,4) and justify the formula area(ABC) = 1 2 det x1 y1 1 x2 y2 1 x3 y3 1 = 1 2 det 2 2 1 1 3 1 1 4 1 Hint: Subtracting the last row from each of the others leaves det 2 2 1 1 3 1 1 4 1 = det 1 6 0 2 7 0 1 4 1 = det" 1 6 2 7#. Sketch A 0 = (1,6), B 0 = (2,7), C 0 = (0,0) and their relation to A, B, C.
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